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<span class="kw">set </span><font color="Maroon" title="c2">A</font> =  the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">O</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P</font>;<br/>
<a NAME="E1:72_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P</font>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">O</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">P</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">P</font> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">O</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">O</font> is  <a href="proofs_1.html#NV14" title="PROOFS_1:NV.14">inconsistent</a> </span><br/>

<a NAME="E3:72_1_1"/>
 for <font color="Olive" title="b1">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c4">O</font> holds <br/><font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c4">O</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Olive" title="b1">a</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="72_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c4">O</font> implies <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c4">O</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Maroon" title="c5">a</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:72_1_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c4">O</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c4">O</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Maroon" title="c5">a</font></span><br/>

<a NAME="E2:72_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="proofs_1.html#U1" title="PROOFS_1:sel.1">Axioms</a> of <font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K8" title="PROOFS_1:func.8">\/</a> <font color="Maroon" title="c4">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T12" onmouseover="rs('xboole_1/T12')" onmouseout="rh()">XBOOLE_1:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:72_1_1_1"/>
<font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c4">O</font> <a href="proofs_1.html#R3" title="PROOFS_1:pred.3">|-</a> <font color="Maroon" title="c5">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="proofs_1.html#T8" target="_self" onmouseover="rs('proofs_1/T8')" onmouseout="rh()">Th46</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E4:72_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">P</font> <a href="proofs_1.html#K9" title="PROOFS_1:func.9">\/</a> <font color="Maroon" title="c4">O</font> is  <a href="proofs_1.html#NV12" title="PROOFS_1:NV.12">inconsistent</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E5:72_1_1"/>
<font color="Maroon" title="c4">O</font> is  <a href="proofs_1.html#NV14" title="PROOFS_1:NV.14">inconsistent</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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